Fast and well-conditioned integral equation solvers for low-frequency electromagnetic problems

2015 ◽  
Author(s):  
Qin Liu
Keyword(s):  
Integral Equation ◽  
Low Frequency ◽  
Electromagnetic Problems

scholarly journals The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1968
Author(s):  
Giovanni Aiello ◽  
Salvatore Alfonzetti ◽  
Santi Agatino Rizzo ◽  
Nunzio Salerno
Keyword(s):  
Integral Equation ◽  
Eddy Currents ◽  
Computing Time ◽  
Low Frequency ◽  
Dirichlet Condition ◽  
Open Boundary ◽  
Coordinate Transformations ◽  
External Layer ◽  
Electromagnetic Problems ◽  
Electrostatic Fields

This paper describes a particular use of the hybrid FEM-DBCI, for the computation of low-frequency electromagnetic fields in open-boundary domains. Once the unbounded free space enclosing the system has been truncated, the FEM is applied to the bounded domain thus obtained, assuming an unknown Dirichlet condition on the truncation boundary. An integral equation is used to express this boundary condition in which the integration surface is selected in the middle of the most external layer of finite elements, very close to the truncation boundary, so that the integral equation becomes quasi-singular. The method is described for the computation of electrostatic fields in 3D and of eddy currents in 2D, but it is also applicable to the solution of other kinds of electromagnetic problems. Comparisons are made with other methods, concluding that FEM-DBCI is competitive with the well-known FEM-BEM and coordinate transformations for what concerns accuracy and computing time.

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